Question

if root ab be an irrational number prove that root a +root b is irrational.

Answer 1

well if sqrt(ab) is irrational,,surely atleast 1 of a and b must not be a perfect square..
which means either sqrt(a) is irrational,,or sqrt(b),,or even both
thus you cant represent there sum into p\q form ..thus sum must be irrational

Answer 2

when there roots is negative.

Answer 3

Given: -\[\sqrt{ab} \rightarrow irrational \rightarrow \sqrt{a}* \sqrt{b}\]
To prove: -\[\sqrt{a}+\sqrt{b} \rightarrow irrational\]Now looks better lol :)

Answer 4

Proof: - ????????????

Answer 5

Proof is given as follows: -

Answer 6

Let \[\sqrt{a}+\sqrt{b} \]rational. then; \[(\sqrt{a}+\sqrt{b})^2=a+b+2\sqrt{ab}\]Should be rational
but \[\sqrt{ab} \]is given irrational
So as a contradiction \[\sqrt{a}+\sqrt{b}\]
must be irrational :D

Answer 7

let c=root of ab, and so c is irrational. so a=c/root of b and b=c/root of a. since an irrational number divided by a rational number will yield a irrational number still, then c/b irrational and c/a is irrational so that root of a and root of b will be irrational and so sum of these two is still irrational